8 



FIVDROnYNAMICS IN SHIP DESIGN 



Srr. -//J 



For a propeller hroiize liaviiiK a weinht density 

 of 519 lb per ft', the mass density p(rho) at sea 

 level is 5 H), 32.174 = 10. 13 slugs per ft'. Assuming 

 that the elastic nuxhilus E of this bronze is 

 15(10*) psi, the celerity r of a shock wave in 

 bronze is 



^ [E. = r i5(10")144 T 

 " \p L 1(3.13 J 



= 1 l,.")7l ft per sec. 



The reiation.ship between the two values of 

 celerity, as a matter of interest, is 1 1,574 4,960 = 

 2.33: 1. 



41.3 The Euler and the Cavitation Numbers. 

 The Euler number K„ , «>r the prc.s.sine cocliicient, 

 as it is also known, is a relationship between 

 pres-sures of the fonn 



^n = 





A p Ap 



P y2 q 



(2.xviii) 



TABLE 41. a — Sum.nhkv of D.\ta on Dimensionless Relatio.vships 



This table is a duplicate of Table 2.a in Volume I, inserted here for the convenience of the reader. 



The ratios of the forces set down in this table follow the listing by J. K. Vennard |"Elemcntary Fluid Meclianica," 

 Wiley, New York, 1947, pp. 144-145] and by H. Rouse (E.MF, 1946, pp. 02, 104, 322, 344). The forces mentioned are unit 

 forces in each case, and the inertia force is the same as the inertia! reaction. 



Name of 

 Relationship 



Symbol 



Mathematical 

 Expression 



Relationship between Physical Quantities 



Mach 



Af. 



U 



Cb 



Velocity of phenomenon 



Ratio of -— — r^ — ;; : in any medium 



Velocity of compression wave 



Cauchy 



C. 



s 



„ . , Inertial reaction . 



Ratio of — in any given medium 



Elasticity force 



Euler 



Cavitation 



Froude 



Reynolds 



Planing 



Stroubal 



Wil 



Ap 



E. 



(sigma) 



p» — e 



VJl ' V^ 



R. 



UL VL UD 



Ln 



u 



•IH-T j W, 



lkMtininfac| 



ylfi 



ih 



VgR„ ' VgRii 



Ratio of 



Accelerative or pressure force 

 Inertial reaction 



Ratio of 



Accelerative or pressure force 

 Inertial reaction 



Inertia force 



Ratio of — : — ; in a deep, unlimited body of liquid 



Gravity force 



Ratio of 



Inertia force 

 Viscosity force 



Ratio of 



Drag force or resistance 

 Dynamic-lift force 



Ratio of 



Longitudinal vorte.K spacin g in a vortex stree t 

 Body diameter transverse to flow 



Ratio of 



Inertial reaction to an accolerative force 

 Surface (tension) force 



Ratio of 



Inert ial reaction within bnundiirioit of dimincl 

 Gravity force of hydraulic rmhua liu 



